NBT-Use+place+value+understanding+&+properties+of+operations+to+perform+multi-digit+arithmetic

4.NBT.4. Fluently add and subtract multi-digit whole numbers using the standard algorithm. 4.NBT.5. Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 4.NBT.6. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. || ===‍‍‍‍‍‍Anchor Standard/Mathematical Practice(s) === MP.2. Reason abstractly and quantitatively. MP.3. Construct viable arguments and critique the reasoning of others. MP.4. Model with mathematics. MP.5. Use appropriate tools strategically. MP.7. Look for and make use of structure. || Use __technology__ tools and skills to reinforce classroom concepts and activities. || ===‍‍‍‍‍‍Revised Bloom's Level of thinking === Remembering Understanding Applying || ===‍‍‍‍‍‍Learning Target/Task Analysis === 4.NBT.4 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Students build on their understanding of addition and subtraction, their use of place value and their <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">flexibility with multiple strategies to make sense of the standard algorithm. They continue to use place <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">value in describing and justifying the processes they use to add and subtract. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">This standard refers to fluency, which means accuracy and efficiency (using a reasonable amount of <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">steps and time), and flexibility (using a variety strategies such as the distributive property, <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">decomposing and recomposing numbers, etc.). This is the first grade level in which students are <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">expected to be proficient at using the standard algorithm to add and subtract. However, other <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">previously learned strategies are still appropriate for students to use. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">When students begin using the standard algorithm their explanation may be quite lengthy. After much <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">practice with using place value to justify their steps, they will develop fluency with the algorithm. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Students should be able to explain why the algorithm works. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">4.NBT.5 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Students who develop flexibility in breaking numbers apart (decomposing numbers) have a better <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">understanding of the importance of place value and the distributive property in multi-digit multiplication. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Students use base ten blocks, area models, partitioning, compensation strategies, etc. when multiplying <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">whole numbers and use words and diagrams to explain their thinking. They use the terms factor and <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">product when communicating their reasoning. Multiple strategies enable students to develop fluency with <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">multiplication and transfer that understanding to division. Use of the standard algorithm for multiplication <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">and understanding why it works, is an expectation in the 5th grade. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">This standard calls for students to multiply numbers using a variety of strategies. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">4.NBT.6 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">In fourth grade, students build on their third grade __work__ with division within 100. Students need <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">opportunities to develop their understandings by using problems in and out of context. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Examples: <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">A 4th grade teacher bought 4 new pencil boxes. She has 260 pencils. She wants to put the pencils in the <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">boxes so that each box has the same number of pencils. How many pencils will there be in each box? <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;"> Using Base 10 Blocks: Students build 260 with base 10 blocks and distribute them into 4 equal <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">groups. Some students may need to trade the 2 hundreds for tens but others may easily recognize <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">that 200 divided by 4 is 50. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;"> Using Place Value: 260 ÷ 4 = (200 ÷ 4) + (60 ÷ 4) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;"> Using Multiplication: 4 x 50 = 200, 4 x 10 = 40, 4 x 5 = 20; 50 + 10 + 5 = 65; so 260 ÷ 4 = 65 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Common Misconceptions: (4.NBT.4-6) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Often students mix up when to 'carry' and when to 'borrow'. Also students often do not notice the <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">need of borrowing and just take the smaller digit from the larger one. Emphasize place value and <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">the meaning of each of the digits. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Specific strategies or students having difficulty with lining up similar place values in numbers as <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">they are adding and subtracting, it is sometimes helpful to have them write their calculations on <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">grid paper. This assists the student with lining up the numbers more accurately. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">If students are having a difficult time with a standard addition algorithm, a possible modification <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">to the algorithm might be helpful. Instead of the 'shorthand' of 'carrying,' students could add by <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">place value, moving left to right placing the answers down below the 'equals' line.
 * ===<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Common Core Standards ===
 * ===<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">‍‍‍‍‍‍Information Technology Standard ===

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">‍‍‍‍‍‍I can...
<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">I can add multi digit whole numbers. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">I can subtract multi digit whole numbers. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">I can multiply a whole number of up to four digits by a one digit number. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">I can multiply a two digit number by a two digit number. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">I can illustrate my multiplication calculations through a variety of methods. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">I can divide up to four digits by one digit using various methods. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">I can recognize the relationship between multiplication and divison.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">‍‍‍‍‍‍Essential Vocabulary
<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">add, subtract, multiply, equations, rectangular arrays, area models, product, quotients, remainders, dividends, divisors, multiplication, division, equations, rectangular arrays, area models

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">‍‍‍‍‍‍Sample Assessments
<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">8 x 8,256 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">87 x 36 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Students will measure the length and width of the classroom and then multiply the dimensions to find the area. Repeat in the hall, the cafeteria, and the playground. Determine the proper unit of measurement to use in each case.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Each year our school has a field day where students rotate between 7 different activities. If the physical education teacher divides the 434 students evenly between the activities, how many students will there be at each activity? Will there be any students left out? Justify your answer.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">‍‍‍‍‍‍Differentiation
<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">‍‍‍‍‍‍Intervention:
<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Use base ten blocks

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Use a deck of cards to practice place value, making biggest/smallest number, etc.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">http://daretodifferentiate.wikispaces.com/Choice+Boards

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">media type="custom" key="19629084"

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">media type="custom" key="19629046"

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">media type="custom" key="19632402"

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">‍‍‍‍‍‍Enrichment:
<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Math24 game cards <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">[]

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Long Division

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">‍‍‍‍‍Instructional Resources
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===<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">‍‍‍‍‍‍Notes and Additional Information ===